Time Series: Practical Issues

class: center, middle, inverse, title-slide

.title[
# Time Series: Practical Issues
]
.subtitle[
## FPP3, Chapter 13
]
.author[
### Robert W. Walker
]
.institute[
### AGSM
]
.date[
### 2022-12-05
]

---

---
# Practical Issues in Forecasting

## Models for different frequencies

---
### Models for annual data

* ETS, ARIMA, Dynamic regression

---
### Models for quarterly data

* ETS, ARIMA/SARIMA, Dynamic regression, Dynamic harmonic regression, STL+ETS, STL+ARIMA

---
### Models for monthly data

* ETS, ARIMA/SARIMA, Dynamic regression, Dynamic harmonic regression, STL+ETS, STL+ARIMA

---
### Models for weekly data

* ARIMA/SARIMA, Dynamic regression, Dynamic harmonic regression, STL+ETS, STL+ARIMA, TBATS

---
### Models for daily, hourly and other sub-daily data

* ARIMA/SARIMA, Dynamic regression, Dynamic harmonic regression, STL+ETS, STL+ARIMA, TBATS

---
# Ensuring forecasts stay within limits

---
## Positive forecasts: Use logs

```r
library(fpp3)
recent_prices <- fpp3::prices %>% filter(!is.na(eggs)) %>% as_tsibble(index=year) %>% select(year, eggs)
recent_prices %>%
  model(ETS(log(eggs) ~ error("A") + trend("A") + season("N"))) %>%
  forecast(h=50) %>%
  autoplot(eggs)
```

---
# Combining Forecasts
## Forecast combinations
### Clemen (1989)

"The results have been virtually unanimous: combining multiple forecasts leads to increased forecast accuracy. `$\dots$` In many cases one can make dramatic performance improvements by simply averaging the forecasts."

---
## Forecast combinations

```r
aus_cafe <- aus_retail %>%
  filter(Industry == "Cafes, restaurants and catering services") %>%
  summarise(Turnover = sum(Turnover))
fc <- aus_cafe %>%
  filter(Month <= yearmonth("2013 Sep")) %>%
  model(
    ETS = ETS(Turnover),
    ARIMA = ARIMA(Turnover)
  ) %>%
  mutate(
    Combination = (ETS + ARIMA)/2
  ) %>%
  forecast(h = 60)
```

---
## Forecast combinations

```r
fc %>% autoplot(aus_cafe, level = NULL) +
  labs(x = "Year", y = "$ billion",
       title = "Australian monthly expenditure on eating out")
```

---
## Forecast combinations

```r
fc %>% accuracy(aus_cafe)
```

---
# Missing Values

**Functions which can handle missing values**

* `ARIMA()`
 * `TSLM()`
 * `NNETAR()`
 * `VAR()`
 * `FASSTER()`

**Models which cannot handle missing values**

* `ETS()`
 * `STL()`
 * `TBATS()`
 
---
### What to do?

1. Model section of data after last missing value.
 2. Estimate missing values with `interpolate()`.
 
---
## Missing values

```r
gold <- as_tsibble(forecast::gold)
gold %>% autoplot(value)
```

---
## Missing values

```r
gold_complete <- gold %>%
  model(ARIMA(value)) %>%
  interpolate(gold)
gold_complete %>%
  autoplot(value, colour = "red") +
  autolayer(gold, value)
```

---
## Outliers

```r
fit <- gold %>%
  model(ARIMA(value))
augment(fit) %>%
  mutate(stdres = .resid/sd(.resid, na.rm=TRUE)) %>%
  filter(abs(stdres) > 10)
```

```
# A tsibble: 2 x 7 [1]
# Key:       .model [1]
  .model       index value .fitted .resid .innov stdres
  <chr>        <dbl> <dbl>   <dbl>  <dbl>  <dbl>  <dbl>
1 ARIMA(value)   770  594.    499.   94.7   94.7   16.4
2 ARIMA(value)   771  487.    562.  -74.8  -74.8  -12.9
```